Abstract
As representatives of a basal bird lineage, pigeons have exhibited remarkable visual numerical cognition, comparable even to that of monkeys. Nevertheless, whether visual numerical cognition in pigeons conforms to the Weber-Fechner law remains unknown. To address this, we designed a fully automated apparatus tailored for pigeons and used it to train them to perform a delayed match-to-numerosity task. The results showed that on a linear scale, pigeons represented smaller numerosities with higher precision and larger numerosities with lower precision, exhibiting a numerical magnitude effect. When the linear scale was compressed into a logarithmic scale, this magnitude effect was offset, resulting in similar representational characteristics across different numerosities. This finding suggests that the mental number line of pigeons is logarithmic rather than linear, consistent with the Weber-Fechner law. While biological brains seek precision in representing numerical information, they must also take computational load into account. This representational strategy may be the optimal outcome of the trade-off between computational precision and computational load that biological brains have achieved through long-term evolution.